We discuss an efficient higher order finite difference algorithm for solving systems of 3-D reaction–diffusion equations with nonlinear reaction terms. The algorithm is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular seven-point difference stencil similar to that used in the standard second-order algorithms, such as the Crank–Nicolson algorithm. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

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This research was supported in part by the Visiting Scholar Foundation of University Key Laboratories in China, and by the United States National Science Foundation under Grant DMS 0075009.